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Subtracting negative fractions

Integer Rules

One page, every sign rule: how positive and negative numbers combine under addition, subtraction, multiplication, and division — each with a fraction example, because signed fractions follow the identical tables.

  • sign rules reference
  • all four operations
  • same signs, different signs
  • add the opposite
Start with what negative fractions are

Quick answer

Two ideas generate every rule

For adding and subtracting, think direction: positive numbers walk right of zero, negative numbers walk left, and the answer is where you land. For multiplying and dividing, think counting: an even number of negative signs cancels to positive, an odd number leaves the answer negative.

Subtraction has no rule of its own — it rewrites as adding the opposite. That single move (keep the first number, change the operation, change the second number’s sign) turns every subtraction into an addition the direction rules already handle.

The reference table

All four operations with signed numbers

Each row states the rule, one integer example, and one fraction example that follows the identical sign logic. The fraction column always ends in standard form: sign in front, positive denominator, simplified.

OperationRuleInteger exampleFraction example
AdditionSame signs: add the sizes, keep the sign. Different signs: subtract the sizes, keep the larger one’s sign.-4 + 9 = 5-3/4 + 1/2 = -1/4
SubtractionAdd the opposite: keep the first number, change − to +, change the second number’s sign.-5 - (-9) = -5 + 9 = 4-1/2 - (-3/4) = 1/4
MultiplicationMultiply the sizes. An even number of negative signs gives a positive product; an odd number gives a negative product.-3 × -4 = 12-2/3 × 3/5 = -2/5
DivisionSame sign table as multiplication, because dividing is multiplying by the reciprocal.-12 ÷ -4 = 3-3/4 ÷ 1/2 = -3/2

Quick checks

Eight problems that test every rule

Cover the right two columns, work each problem, then check the answer and the reason. If a reason does not match the rule you used, the rule — not the arithmetic — needs another look.

ProblemAnswerWhy
7 + (-3)4Different signs: 7 outgrows 3, positive wins.
-7 + 3-4Different signs: 7 outgrows 3, negative wins.
-7 - (-3)-4Add the opposite: -7 + 3.
-7 × -321Two negatives cancel in multiplication.
-7 × 3-21One negative sign survives.
-7 ÷ -37/3 = 2 1/3Two negatives cancel; the quotient is positive.
-3/4 - (-1/4)-1/2Minus a minus becomes plus: -3/4 + 1/4.
-2/3 × -3/52/5Two signs cancel, then multiply across.

Five memory hooks that survive the test

  • Counting rule: for × and ÷, count the negative signs — even means positive, odd means negative.
  • Direction rule: for + and −, picture the number line — positive walks right, negative walks left, and the last step lands on the answer.
  • Rewrite rule: every subtraction is adding the opposite, so minus a minus is always a plus.
  • Standard-form rule: finish every fraction with a positive denominator — 6/-4 is unfinished, -6/4 or -3/2 is finished.
  • Size rule: signs never change sizes, only direction — compare -3/4 with 3/4 and only the side of zero differs.

Why the tables stay the same for fractions

A signed fraction is an ordinary fraction with a direction attached. The sign lives with the whole value, so every operation first asks its usual sign question — combine directions for addition and subtraction, count factors of -1 for multiplication and division — and then runs the familiar size work: common denominators, keep-change-flip, simplify.

That layering is why this page pairs with every negative-fraction topic. When a signed fraction problem goes wrong, the error almost always sits in one identifiable layer: a sign miscounted, a sign dropped during a flip, or a denominator left negative in the final answer. Naming the layer turns a vague “I got it wrong” into a specific habit to fix.

See the sign count applied to products and quotients

Keep learning

Related fraction topics

What Are Negative Fractions?Why Integer Signs SwitchNegative Denominator Rules

Common questions

Integer Rules FAQ

Addition: same signs add and keep the sign; different signs subtract the smaller size and keep the larger one’s sign. Subtraction: add the opposite. Multiplication and division: count the negative signs — an even count gives a positive result, an odd count gives a negative one.